International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,
http://iraj.in
Volume- 5, Issue-2, Feb.-2017
USING FITNESS FUNCTION TO SOLVE TWO-SIDED ASSEMBLY
LINE BALANCING BY SPREAD SHEET
1
S. A. ELTERIKI, 2S. A. BAREDUAN, 3M. F. M. A. HAMZAS
1,2,3
Department of manufacturing and industrial engineering, University Tun Hussein Onn Malaysia
E-mail: [email protected]
Abstract— In this paper, the solution of two-sided assembly line balancing is conducted by using spread sheet model, in order
to simplify the complex problem by way of simple code. The fitness function has been executed to evaluate the variety of
solutions of two-sided assembly line balancing. With the objective to minimize the number of work stations, the random rule
is run up to the maximum number of iterations, using the proposed method with different cycle times. The relation between
fitness values and number of work stations were evaluated and presented in graph.
Keywords— Two sided assembly line balancing, spread- sheet, fitness function.
Search (TS) algorithm for 2-SALBP considering line
efficiency and smoothness index as performance
criteria was also introduced [9]. The proposed
pre-emptive goal programme for precise goals and a
fuzzy goal programme for imprecise goals were
developed to minimize the number of work stations
[10].
A Mixed Integer Programming (MIP) model was also
investigated and proposed with a Simulated
Annealing (SA) algorithm for solving 2-SALBP to
minimise the number of mated stations [11]. Simaria
and Vilarinho (2009) presented an Ant Colony
Optimization (ACO) algorithm to address the
mixed-model 2-SALBP, and built a balancing solution
that considered precedence, zoning, capacity, and side
and synchronism constraints [15].
The first Bee Algorithm (BA) application to 2-SALBP
and employed fuzzy mathematical programming were
presented to solve the two-sided assembly-line
balancing problem with zoning constraint so as to
minimize the number of stations for a given cycle
time. An extensive computational study was carried
out and the results were compared with the results of
several algorithms from the literature such as ant
colony optimization and tabu search.
The two-sided assembly-line balancing problem is
considered more realistic by employing positional,
zoning and synchronous task constraints and by
utilizing fuzzy approaches so as to maximize both
work slackness index and line efficiency and
minimize total balance delay. Bees Algorithm was
used as a search mechanism for obtaining good
solutions, extensive computational results were then
presented [13].
Several researchers introduced a mixed integer,
non-linear programming model for fully constrained
in order to describe the problem formally. Due to the
complexity of the problem, swarm intelligence based
bee algorithm and Artificial Bee Colony (ABC)
algorithms were implemented to evaluate the
I. INTRODUCTION
Assembly line is widely used in various production
systems. The goals of introducing an assembly line
into a plant are to maximize efficiency and keep
optimum costs. The problem related to optimally
distributing assembly tasks among all workstations
with respect to certain objectives, is called an assembly
line balancing problem (ALBP). Assembly line can be
one-sided or two-sided. One-sided assembly lines are
most widely studied in ALBP while less attention is
paid to two-sided assembly line balancing problems
(2-SALBP). The 2-SALBP is an extension of simple
ALBP when different assembly tasks are carried out
on the same product, in parallel, on both left and
right-hand sides of the line. Compared to simple
assembly line, two-sided assembly lines can shorten
the line length, lower the cost of tools and fixtures, and
reduce material handling and operator movement [1].
Therefore, the 2-SALBP has prominent research
significance and practical value.
In spite of these preface benefits, some complex
restrictions exist when balancing two-sided assembly
lines, such as operation direction constraints,
positional, positive–negative zoning constraints, and
synchronous task constraints. Hence, the 2-SALBP is
much more complex and the development of new
balancing techniques is needed. The design and
balancing of two-sided assembly lines was first studied
by Bartholdi [1] using a balancing algorithm based on
the first-fit rule (FFR). A Genetic Algorithm (GA) was
applied to solve 2-SALBP with positional constraints
[6] [7]. A branch and bound was introduced as an
algorithm to minimize the line length of a two-sided
assembly line [16]. The station-oriented enumeration
algorithm that was integrated with the Hoffmann
heuristic was also developed to solve 2-SALBP [4].
The first attempt to show how an Ant Colony Heuristic
(ACH) could be applied to solve 2-SALBP with
zoning constraints was discussed in 1998 [2]. Tabu
Using Fitness Function to Solve Two-Sided Assembly Line Balancing by Spread Sheet
26
International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,
http://iraj.in
performance. However, the addition of positional,
zoning and synchronous task constraints constitute
the problem to be much more complex and these
factors were important for practical applications. The
extensive computational study results indicate that BA
and ABC Algorithms obtained approximately the
same results [8] [12].
A simple efficient approach was introduced to
implement the line balancing problem in
spread-sheets by array formula to provide an
interesting and easily understood technique [14]. The
array formula approach with an interesting simple
precedence coding system were combined to present
an efficient spreadsheet for performing assembly line
balancing using priority rules method. This paper
presented task coding to show completed tasks and to
ensure the task will not be scheduled a second time [5].
The simple assembly line balancing by spreadsheet
has been modified to accommodate the methodology
for solving two-sided assembly line balancing
problem. In addition, random task selection was added
to conventional priority rules to present the effect of
multi-solutions on two-sided assembly line balancing.
Tests were conducted to evaluate the performance of
the spreadsheet methodology and the random priority
rule had generated better performance results for the
two-sided assembly line balancing problem [3].
Referring to the literature review, no published paper
has dealt with solution of two-sided assembly line
balancing problems in spreadsheet using Artificial
Bee Colony algorithm with a simple coding system.
This paper presents the result of using such system for
solving the 2-SALBP. The organization of this paper
is as follows: the next section illustrates fitness
function in spread sheet method. Section 4 discusses
the results and last section present conclusion.
Volume- 5, Issue-2, Feb.-2017
Where: n is the number of stations,
ct is the cycle time, Sk is the kth station time.
The first part of fitness function aims to find the best
balance among the solution that have the same
number of stations while the second part minimize the
number of stations in the solutions since the first
objective is arbitrarily assumed to be more critical
than the second, it is multiplied by two.
B. Two-sided assembly line balancing
The two-sided assembly line balancing has two
parallel production lines, on the left and right sides. In
production line for a single product, tasks can be
simultaneously assigned to corresponding stations,
and some specific tasks can be defined for assigned to
matching stations, and some specific tasks can be
defined for assignment to a specific side. For example,
if a task is defined as a left side (L) or right side (R)
task, it can be assigned to the station of the left side or
right side of the production line consequently. Tasks
defined as either side (E) can be assigned to either the
left or right side of the production line. Moreover,
tasks can be appropriately assigned to stations on both
sides for synchronized assembly, thus reducing idle
time without conflicting with the requirement. The
stations of the left and right of the production line are
known as mated-stations (positions), and are of the
same in the cycle time, meaning one side has a
companion relationship with the station on the other
side. In Fig. (1), the number in brackets represent task
time, the English alphabets represent the task
assignment direction (L: left side; R: right side; E:
either side), the numbers in circles represent task
number, the arc is the process assembly precedence,
and the total task time is 25 units. The spread sheet
model is applied on two-sided assembly line balancing
to make efficient and easy coding rather than other
complex programming languages.
II. FITNESS FUNCTION IN SPREAD-SHEET
MODEL
A. Fitness function
The study on two-sided assembly line balancing has
generally focused on minimizing the number of
stations according to a definite cycle time, known as
type-1. The objective of two-sided ALB measured in
this work is to minimize the number of stations for
given cycle time. However, given two different
solutions with same number of work stations, one may
be better balanced than other. Hence we used a fitness
function that consists of two objectives, ie-minimizing
the number of work stations and obtaining balanced
work station.
Fitness function is formally defined as in Eq. (1). [7]
Figure (1) Example of a two-sided line balancing problem
C. Calculation of fitness function
Referring to literature review work on two-side
assembly line balancing by Bareduan and Elteriki
(2015), they applied balancing on two-sided without
considering fitness of 2SALB. To compare between
many solutions with different parameters, this work
(1)
Using Fitness Function to Solve Two-Sided Assembly Line Balancing by Spread Sheet
27
International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,
http://iraj.in
introduces the fitness function (1) in spread sheet to
show the significance deferent between solutions and
choose the feasible one which has minimum fitness
value, especially if the solutions have the same work
stations. Fig. (2) illustrates one solution of the
problem shown in the network of Fig. (1). The steps
involved are assigning the tasks to stations on both
sides, calculate the tasks operation times in every
station, subtract total operation time from cycle time
Volume- 5, Issue-2, Feb.-2017
and apply the results on equation (1) to get fitness of
solution of two-sided assembly line balancing.
D. Computational results in spreadsheet
The assigning of tasks on left side appear in cells E176
to P176. Similarly on right side is from cells E180 to
P180. To calculate the fitness function of this solution,
the tasks and operation times should be rearranged
corresponding to work station before calculating total
idle times to every work station. Then the fitness can
be calculated as shown in Fig.(2) in cell S205.
Figure (2) Example of fitness calculation in two-sided line balancing problem
Fig. (3) The relation between work station and fitness
Table (1) the range of fitness value with ideal time and statistical parameters
solutions have different work station corresponding to
fitness results, the minimum work station is 5 related
to minimum fitness of 3.366 among 100 trial limit.
The graph in Fig. (3) Shows the direct proportional
relation between the number of work stations and
fitness through the number of trial. The correlation
III. DISCUSSION OF RESULTS
The example problem in Figure (2) was used to
generate several solutions, and calculation of fitness in
two-sided assembly line balancing solutions using a
spreadsheet. Using the cycle time of 6 minutes, the
Using Fitness Function to Solve Two-Sided Assembly Line Balancing by Spread Sheet
28
International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,
Volume- 5, Issue-2, Feb.-2017
http://iraj.in
[3] Bareduan,S.A., & Elteriki,S.A. “Methodology for solving
value is 0.94. Table (1) illustrates statistical analysis by
two-sided assembly line balancing in spreadsheet”. Journal of
spread sheet, the minimum fitness value with
ENGINEERING AND Applied Sciences, vol.11,No.10,May
minimum work stations have low standard division of
2016.
[4] Hu, X., Wu, E., & Jin, Y. A station-oriented enumerative
idle time, which means upright balancing of each work
algorithm for two-sided assembly line balancing. European
station.
Journal of Operational Research, 186(1),435–440, (2008).
[5] Howard J. Weiss ”Implementing Line Balancing Heuristics in
Spreadsheets”.INFORMS Transactions on Education.
CONCLUSION
13(2),pp.114-125,(2013).
[6] Kim, Y. K., Kim, Y., & Kim, Y. J. Two-sided assembly line
This paper introduced an effective approach for
balancing: A genetic algorithm approach. Production,
Planning and Control, 11, 44–53, (2000).
calculating fitness function in spread sheet to get
[7] Kim, Y. K., Song, W. S., & Kim, J. H. A mathematical model
feasible solution of two-sided assembly line balancing.
and a genetic algorithm for two-sided assembly line balancing.
The two-sided assembly line dealt with in this paper
Computers and Operations Research, 36, 853–865, (2009).
[8] Lale Ozbakir, Pınar Tapkan “Bee colony intelligence in zone
are simple in that it considers the spread sheet coding ,
constrained two-sided assembly line balancing problem”.
easy for obtaining new solutions with deferent results
Expert
Systems with Applications Vol.38, pp.
such as number of stations and fitness value. There is
11947–11957,(2011).
direct relation between number of work stations and
[9] Ozcan, U., & Toklu, B. A tabu search algorithm for two-sided
assembly line balancing. International Journal of Advanced
fitness value among number of runs with fixed cycle
Manufacturing Technology, 43(7–8), 822, (2009a).
time. The solution has minimum fitness function as
[10] Ozcan, U., & Toklu, B. (2009b). Multiple-criteria
well have good distribution of idle time among
decision-making in two-sided assembly line balancing: A goal
programming and a fuzzy goal programming models.
workstation. For future work, it is worth to consider
Computers and Operations Research, 36, 1955–1965.
application of other constraints such as position,
[11] Ozcan, U., & Toklu, B. Balancing of mixed-model two-sided
zoning and synchronous on two-sided assembly line
assembly lines. Computers and Industrial Engineering, 57,
217–227,(2009c).
balancing in spread sheet to make it more applicable in
[12] Pinar Tapkan, Lale Ozbakir, Adil Baykasoglu, “Modeling
meta- heuristic.
and solving constrained two-sided assembly line balancing
problem via bee algorithms”. Applied Soft Computing Vol.12,
pp.3343–3355. Advanced Manufacturing Technology
ACKNOWLEDGMENTS
011;53:363–78, (2012).
[13] P. Tapkan, A. Baykasoglu, L. Ozbakir, , Bees algorithm for
This publication is partially supported by Fundamental
fuzzy multi-objective two-sided fuzzy assembly line balancing
problem.I.B. Turksen (Eds.), Proceedings of 1st International
Research Grant Scheme of Malaysia No.1497(2/2014)
Fuzzy Systems Symposium, TOBB Economy and Technology
and Centre Post Graduate Studies Centre of Universiti
University, Ankara, Turkey, pp. 203–210,2011.
Tun Hussein Onn Malaysia.
[14] Ragsdale,C. T., E. C. Brown. On modelling line balancing
problems in spreadsheets. INFORMS Transactions Education.
4(2) 45-48, 2004.
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